99 accepted papers
This paper studies optimization for a family of problems termed **compositional entropic risk minimization**, in which each data's loss is formulated as a Log-Expectation-Exponential (Log-E-Exp) function. The Log-E-Exp formulation serves as an abstraction of the Log-Sum-Exponential (LogSumExp) funct…
As tropical cyclones intensify and track forecasts become increasingly uncertain, U.S. ports face heightened supply-chain risk under extreme weather conditions. Port operators need to rapidly synthesize diverse multimodal forecast products, such as probabilistic wind maps, track cones, and official
Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long and redundant reasoning even for simple questions, which su…
Accurately estimating the normalization term (also known as the partition function) in the contrastive loss is a central challenge for training Contrastive Language-Image Pre-training (CLIP) models. Conventional methods rely on large batches for approximation, demanding substantial computational res…
Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood; (ii) available generalization bounds deteriorate as the num…
This paper studies a class of convex Finite-sum Coupled Compositional Optimization (cFCCO) problems with applications including group distributionally robust optimization (GDRO) and learning with imbalanced data. To better address these problems, we introduce an efficient single-loop primal-dual blo…
Contrastive Language-Image Pre-training (CLIP) generates versatile multimodal embeddings for diverse applications, yet the specific information captured within these representations is not fully understood. Current explainability techniques often target specific tasks, overlooking the rich, general…
The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitat…
In self-supervised contrastive learning, negative pairs are typically constructed using an anchor image and a sample drawn from the entire dataset, excluding the anchor. However, this approach can result in the creation of negative pairs with similar semantics, referred to as "false negatives", lead…
Supervised fine-tuning (SFT) has become a crucial step for aligning pretrained large language models (LLMs) using supervised datasets of input-output pairs. However, despite being supervised, SFT is inherently limited by its generative training objective. To address its limitations, the existing com…
Regression is a fundamental task in machine learning that has garnered extensive attention over the past decades. The conventional approach for regression involves employing loss functions that primarily concentrate on aligning model prediction with the ground truth for each individual data sample.…
This paper formalizes an emerging learning paradigm that uses a trained model as a reference to guide and enhance the training of a target model through strategic data selection or weighting, named **model steering**. While ad-hoc methods have been used in various contexts, including the training of…
We study the discriminative probabilistic modeling on a continuous domain for the data prediction task of (multimodal) self-supervised representation learning. To address the challenge of computing the integral in the partition function for each anchor data, we leverage the multiple importance sampl…
Despite its empirical success, the theoretical foundations of self-supervised contrastive learning (CL) are not yet fully established. In this work, we address this gap by showing that standard CL objectives implicitly approximate a supervised variant we call the negatives-only supervised contrastiv…
Finite-sum Coupled Compositional Optimization (FCCO), characterized by its coupled compositional objective structure, emerges as an important optimization paradigm for addressing a wide range of machine learning problems. In this paper, we focus on a challenging class of non-convex non-smooth FCC…
Reinforcement learning from human feedback (RLHF) is a prevalent approach to align AI systems with human values by learning rewards from human preference data. Due to various reasons, however, such data typically takes the form of rankings over pairs of trajectory segments, which fails to capture th…
Federated learning faces challenges due to the heterogeneity in data volumes and distributions at different clients, which can compromise model generalization ability to various distributions. Existing approaches to address this issue based on group distributionally robust optimization (GDRO) often…
In this paper, we study a class of non-smooth non-convex problems in the form of $\min_{x}[\max_{y\in\mathcal Y}\phi(x, y) - \max_{z\in\mathcal Z}\psi(x, z)]$, where both $\Phi(x) = \max_{y\in\mathcal Y}\phi(x, y)$ and $\Psi(x)=\max_{z\in\mathcal Z}\psi(x, z)$ are weakly convex functions, and $\phi(…
Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization and meta-learning, where the objective function involves a nested composition associated with an expectation. Although many studies have been devote…
The temperature parameter plays a profound role during training and/or inference with large foundation models (LFMs) such as large language models (LLMs) and CLIP models. Particularly, it adjusts the logits in the softmax function in LLMs, which is crucial for next token generation, and it scales th…
In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of…
In this paper, we tackle a novel federated learning (FL) problem for optimizing a family of X-risks, to which no existing FL algorithms are applicable. In particular, the objective has the form of $\mathbb{E}\_{\mathbf{z}\sim \mathcal{S}\_1} f(\mathbb{E}\_{\mathbf{z}'\sim\mathcal{S}\_2} \ell(\mathbf…
Federated learning has attracted increasing attention due to the promise of balancing privacy and large-scale learning; numerous approaches have been proposed. However, most existing approaches focus on problems with balanced data, and prediction performance is far from satisfactory for many real-wo…
Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular, the existing generalization error bounds depend linearly on th…
We study a family of loss functions named label-distributionally robust (LDR) losses for multi-class classification that are formulated from distributionally robust optimization (DRO) perspective, where the uncertainty in the given label information are modeled and captured by taking the worse case…
Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation (NCE) has been proposed by formulating the objective as the logistic loss of the real…
This paper seeks to address a gap in optimizing Average Precision (AP) while ensuring adversarial robustness, an area that has not been extensively explored to the best of our knowledge. AP maximization for deep learning has widespread applications, particularly when there is a significant imbalance…
This paper investigates new families of compositional optimization problems, called non-smooth weakly-convex finite-sum coupled compositional optimization (NSWC FCCO). There has been a growing interest in FCCO due to its wide-ranging applications in machine learning and AI, as well as its ability to…
In this paper, we aim to optimize a contrastive loss with individualized temperatures in a principled manner. The common practice of using a global temperature parameter $\tau$ ignores the fact that ``not all semantics are created equal", meaning that different anchor data may have different numbers…
This paper considers a novel application of deep AUC maximization (DAM) for multi-instance learning (MIL), in which a single class label is assigned to a bag of instances (e.g., multiple 2D slices of a CT scan for a patient). We address a neglected yet non-negligible computational challenge of MIL i…
The problem of urban event ranking aims at predicting the top-$k$ most risky locations of future events such as traffic accidents and crimes. This problem is of fundamental importance to public safety and urban administration especially when limited resources are available. The problem is, however,…
This paper investigates group distributionally robust optimization (GDRO), with the purpose to learn a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem, and demonstrate that stochastic mirror descent (SMD), using…
As machine learning being used increasingly in making high-stakes decisions, an arising challenge is to avoid unfair AI systems that lead to discriminatory decisions for protected population. A direct approach for obtaining a fair predictive model is to train the model through optimizing its predict…
Recently, several universal methods have been proposed for online convex optimization, and attain minimax rates for multiple types of convex functions simultaneously. However, they need to design and optimize one surrogate loss for each type of functions, making it difficult to exploit the structure…
Recently, deep AUC maximization (DAM) has achieved great success in different domains (e.g., medical image classification). However, the end-to-end training for deep AUC maximization still remains a challenging problem. Previous studies employ an ad-hoc two-stage approach that first trains the netw…
This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index. We refer to this family of problems as finite-sum coupled compositional optimization (FCCO). It has broad applications in…
Training of graph neural networks (GNNs) for large-scale node classification is challenging. A key difficulty lies in obtaining accurate hidden node representations while avoiding the neighborhood explosion problem. Here, we propose a new technique, named feature momentum (FM), that uses a momentum…
The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in…
NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to…
In this paper, we study stochastic optimization of areas under precision-recall curves (AUPRC), which is widely used for combating imbalanced classification tasks. Although a few methods have been proposed for maximizing AUPRC, stochastic optimization of AUPRC with convergence guarantee remains an u…
In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual variables and lower level problems. Due to the intertwined mult…
Variance reduction techniques such as SPIDER/SARAH/STORM have been extensively studied to improve the convergence rates of stochastic non-convex optimization, which usually maintain and update a sequence of estimators for a single function across iterations. What if we need to track multiple functi…
In this paper, we investigate the problem of stochastic multi-level compositional optimization, where the objective function is a composition of multiple smooth but possibly non-convex functions. Existing methods for solving this problem either suffer from sub-optimal sample complexities or need a h…
In this paper, we study contrastive learning from an optimization perspective, aiming to analyze and address a fundamental issue of existing contrastive learning methods that either rely on a large batch size or a large dictionary of feature vectors. We consider a global objective for contrastive le…
In this paper, we investigate an online prediction strategy named as Discounted-Normal-Predictor [Kapralov and Panigrahy, 2010] for smoothed online convex optimization (SOCO), in which the learner needs to minimize not only the hitting cost but also the switching cost. In the setting of learning wit…
In this paper, we propose systematic and efficient gradient-based methods for both one-way and two-way partial AUC (pAUC) maximization that are applicable to deep learning. We propose new formulations of pAUC surrogate objectives by using the distributionally robust optimization (DRO) to define the…
In this paper, we propose a practical online method for solving a class of distributional robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural networks. In the literature, most methods for solving DRO are ba…
Deep AUC (area under the ROC curve) Maximization (DAM) has attracted much attention recently due to its great potential for imbalanced data classification. However, the research on Federated Deep AUC Maximization (FDAM) is still limited. Compared with standard federated learning (FL) approaches that…
Deep AUC Maximization (DAM) is a new paradigm for learning a deep neural network by maximizing the AUC score of the model on a dataset. Most previous works of AUC maximization focus on the perspective of optimization by designing efficient stochastic algorithms, and studies on generalization perform…
In many sequential decision making applications, the change of decision would bring an additional cost, such as the wear-and-tear cost associated with changing server status. To control the switching cost, we introduce the problem of online convex optimization with continuous switching constraint, w…
In this paper, we revisit the problem of smoothed online learning, in which the online learner suffers both a hitting cost and a switching cost, and target two performance metrics: competitive ratio and dynamic regret with switching cost. To bound the competitive ratio, we assume the hitting cost is…
Pairwise learning refers to learning tasks where the loss function depends on a pair of instances. It instantiates many important machine learning tasks such as bipartite ranking and metric learning. A popular approach to handle streaming data in pairwise learning is an online gradient descent (OG…
Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the convergence behavior of their stochastic gradient-type algori…
Areas under ROC (AUROC) and precision-recall curves (AUPRC) are common metrics for evaluating classification performance for imbalanced problems. Compared with AUROC, AUPRC is a more appropriate metric for highly imbalanced datasets. While stochastic optimization of AUROC has been studied extensivel…
Generative Adversarial Networks (GANs) are a powerful class of generative models in the deep learning community. Current practice on large-scale GAN training utilizes large models and distributed large-batch training strategies, and is implemented on deep learning frameworks (e.g., TensorFlow, PyTor…
Deep metric learning (DML) has received much attention in deep learning due to its wide applications in computer vision. Previous studies have focused on designing complicated losses and hard example mining methods, which are mostly heuristic and lack of theoretical understanding. In this paper, we…
Abstract.Deep learning has achieved remarkable success in many classification tasks because of its great power of representation learning for complex data. However, it remains challenging when extending to classification tasks with millions of classes. Previous studies are focused on solving this pr…
In this paper, we study distributed algorithms for large-scale AUC maximization with a deep neural network as a predictive model. Although distributed learning techniques have been investigated extensively in deep learning, they are not directly applicable to stochastic AUC maximization with deep ne…
Current deep neural networks can achieve remarkable performance on a single task. However, when the deep neural network is continually trained on a sequence of tasks, it seems to gradually forget the previous learned knowledge. This phenomenon is referred to as catastrophic forgetting and motivates…
Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this limitation, new performance measures, including dynamic regr…
Epoch gradient descent method (a.k.a. Epoch-GD) proposed by (Hazan and Kale, 2011) was deemeda breakthrough for stochastic strongly convex minimization, which achieves theoptimal convergence rate of O(1/T) with T iterative updates for the objective gap. However, its extension to solving stochastic m…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed with theoretical convergence guarantees for non-convex unconstr…
Stochastic AUC maximization has garnered an increasing interest due to better fit to imbalanced data classification. However, existing works are limited to stochastic AUC maximization with a linear predictive model, which restricts its predictive power when dealing with extremely complex data. In th…
In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex func…
Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max probl…
In this paper, we present a novel robust zero- sum game framework for pool-based active learning grounded on advanced statistical learning theory. Pool-based active learning usually consists of two components, namely, learning of a classifier given labeled data and querying of unlabeled data for lab…
Designing the structure of neural networks is considered one of the most challenging tasks in deep learning, especially when there is few prior knowledge about the task domain. In this paper, we propose an Ecologically-Inspired GENetic (EIGEN) approach that uses the concept of succession, extinction…
An important class of non-convex objectives that has wide applications in machine learning consists of a sum of $n$ smooth functions and a non-smooth convex function. Tremendous studies have been devoted to conquering these problems by leveraging one of the two types of variance reduction techniques…
Learning with a convex loss function has been a dominating paradigm for many years. It remains an interesting question how non-convex loss functions help improve the generalization of learning with broad applicability. In this paper, we study a family of objective functions formed by truncating tra…
Stochastic Proximal Gradient (SPG) methods have been widely used for solving optimization problems with a simple (possibly non-smooth) regularizer in machine learning and statistics. However, to the best of our knowledge no non-asymptotic convergence analysis of SPG exists for non-convex optimizati…
Stagewise training strategy is widely used for learning neural networks, which runs a stochastic algorithm (e.g., SGD) starting with a relatively large step size (aka learning rate) and geometrically decreasing the step size after a number of iterations. It has been observed that the stagewise S…
Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC functions have been extensively studied, stochastic optimization th…
Although stochastic gradient descent (SGD) method and its variants (e.g., stochastic momentum methods, AdaGrad) are algorithms of choice for solving non-convex problems (especially deep learning), big gaps still remain between the theory and the practice with many questions unresolved. For example,…
In this paper, we present a simple analysis of fast rates with high probability of empirical minimization for it stochastic composite optimization over a finite-dimensional bounded convex set with exponential concave loss functions and an arbitrary convex regularization. To the best of our knowle…
Negative curvature descent (NCD) method has been utilized to design deterministic or stochastic algorithms for non-convex optimization aiming at finding second-order stationary points or local minima. In existing studies, NCD needs to approximate the smallest eigen-value of the Hessian matrix with a…
To cope with changing environments, recent developments in online learning have introduced the concepts of adaptive regret and dynamic regret independently. In this paper, we illustrate an intrinsic connection between these two concepts by showing that the dynamic regret can be expressed in terms of…
Error bound conditions (EBC) are properties that characterize the growth of an objective function when a point is moved away from the optimal set. They have recently received increasing attention in the field of optimization for developing optimization algorithms with fast convergence. However,…
In this paper, we consider statistical learning with AUC (area under ROC curve) maximization in the classical stochastic setting where one random data drawn from an unknown distribution is revealed at each iteration for updating the model. Although consistent convex surrogate losses for AUC maximiza…
In this paper, we consider online F-measure optimization (OFO). Unlike traditional performance metrics (e.g., classification error rate), F-measure is non-decomposable over training examples and is a non-convex function of model parameters, making it much more difficult to be optimized in an online…
(This is a theory paper) In this paper, we consider first-order methods for solving stochastic non-convex optimization problems. The key building block of the proposed algorithms is first-order procedures to extract negative curvature from the Hessian matrix through a principled sequence starting fr…
The large volume of video content and high viewing frequency demand automatic video summarization algorithms, where a key property is the capability of modeling diversity. If videos are lengthy like hours-long egocentric videos, it is necessary to track the temporal structures of the videos and enfo…
It is now much easier than ever before to produce videos. While the ubiquitous video data is a great source for information discovery and extraction, the computational challenges are unparalleled. Automatically summarizing the videos has become a substantial need for browsing, searching, and indexin…
We consider the constrained optimization where the objective function and the constraints are defined as summation of finitely many loss functions. This model has applications in machine learning such as Neyman-Pearson classification. We consider two level-set methods to solve this class of problems…
Although the convergence rates of existing variants of ADAGRAD have a better dependence on the number of iterations under the strong convexity condition, their iteration complexities have a explicitly linear dependence on the dimensionality of the problem. To alleviate this bad dependence, we propos…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a linear optimization under the inequality constraint are time-cons…
Alternating direction method of multipliers (ADMM) has received tremendous interest for solving numerous problems in machine learning, statistics and signal processing. However, it is known that the performance of ADMM and many of its variants is very sensitive to the penalty parameter of a quadrat…
Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC). However, the faster convergence of restarting APG method relies…
Error bound, an inherent property of an optimization problem, has recently revived in the development of algorithms with improved global convergence without strong convexity. The most studied error bound is the quadratic error bound, which generalizes strong convexity and is satisfied by a large fa…
Recently, there has been a growing research interest in the analysis of dynamic regret, which measures the performance of an online learner against a sequence of local minimizers. By exploiting the strong convexity, previous studies have shown that the dynamic regret can be upper bounded by the path…
In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal solutions. In particular, if the objective function $F(\mathb…
In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The bes…
Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However, the independent sampling for dropout could be suboptim…
Attributes possess appealing properties and benefit many computer vision problems, such as object recognition, learning with humans in the loop, and image retrieval. Whereas the existing work mainly pursues utilizing attributes for various computer vision problems, we contend that the most basic pr…
In this paper, we study a special bandit setting of online stochastic linear optimization, where only one-bit of information is revealed to the learner at each round. This problem has found many applications including online advertisement and online recommendation. We assume the binary feedback is a…
This work focuses on dynamic regret of online convex optimization that compares the performance of online learning to a clairvoyant who knows the sequence of loss functions in advance and hence selects the minimizer of the loss function at each step. By assuming that the clairvoyant moves slowly (i.…
In this paper, we consider the problem of recovering the s largest elements of an arbitrary vector from noisy measurements. Inspired by previous work, we develop an homotopy algorithm which solves the \ell_1-regularized least square problem for a sequence of decreasing values of the regularization p…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling probabilities. The sampling dependent error bound (i) allows us to be…
Deep convolutional neural networks (CNN) have seen tremendous success in large-scale generic object recognition. In comparison with generic object recognition, fine-grained image classification (FGIC) is much more challenging because (i) fine-grained labeled data is much more expensive to acquire (u…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge…